This invention relates to an apparatus for measuring the absolute reflectance of a sample, which employs an integrating sphere.
There are two methods of measuring the reflectance of a sample. One is to measure the relative reflectance of a given sample material to be measured, with the known reflectance of a standard or reference material being taken as 100%, and the other is to measure the true or absolute reflectance of a sample material.
Usually, the relative reflectance of a given sample material (to be referred to as a sample) is first measured and the measured value is multiplied by the absolute reflectance of a reference material (to be referred to as a reference) so as to obtain the absolute reflectance of the sample under measurement. However, the absolute reflectance of the reference is given merely as one of various data and if the reflectance changes as time passes, such changes are not known to the person who is conducting the measurement, so that it is impossible to measure the absolute reflectance of the sample.
The principle of measuring absolute reflectance is simple, but great difficulties are encountered in putting it into practice. One known method of measuring the absolute reflectance of a sample employs an integrating sphere. The method is somewhat complicated in theory but relatively easy to put into practice. In the method which employs an integrating sphere, however, since it is necessary to move the photodetector or the optical path relative to the integrating sphere, a complicated mechanism is required for effecting the relative movement so that the whole structure of the apparatus becomes of a large size. Although the apparatus may be used in a laboratory, it is not suitable for practical use, and it is even more difficult to design the apparatus as an adaptor for ready use in a spectrophotometer.
The principle of measurement of absolute reflectance will first be explained with reference to FIG. 1. There is shown an integrating sphere IS provided with an inlet window WI, through which a light beam Li from a monochromator MC is introduced into the integrating sphere so as to directly illuminate a region Wa on the inner surface of the integrating sphere. The integrating sphere is also formed with a sample window Ws and a pair of outlet windows WOs and WOr. A sample SM is set in the sample window Ws so as to face inwardly of the integrating sphere, and the sample beam Ls comes out of the window WOs and the reference beam Lr, out of the window WOr.
Inside the integrating sphere there is provided a screen SC so arranged as to prevent the light which enters the integrating sphere through the window WI and is reflected directly by the region Wa, that is, the light of the first reflection on the region Wa from striking the sample set in the window Ws. The screen SC is provided at such a position that it cannot be seen through the light measuring system at either one of the outlet windows WOs and WOr. In FIG. 1, for example, the reference light beam Lr is being measured, with a lens LN forming an image of a region Wr on the inner surface of the integrating sphere IS diametrically opposite the outlet window WOr on an aperture AP disposed in front of a photodetector PD. The region Wr is conjugate with the aperture AP and the screen SC is completely out of the optical path of the light Lr which forms the image of the region Wr on the aperture AP. The inner surface of the integrating sphere IS has a uniform, high reflectance r. The screen SC is so painted that its reflectance also is r.
Let the amount of the light Li that enters the integrating sphere IS be expressed by P; the area of the inner surface of the sphere, by S; the area of the window WOr and that of the window WOs, both by b; the area of the sample window Ws and that of the region Wr, both by a; the reflectance of a sample, by r'; and a/S=k.sub.1 and b/S=k.sub.2.
The above-mentioned reflectances r and r' are absolute reflectances.
With a sample SM to be measured having been set in the sample window Ws as shown in FIG. 1, the light Lr emerging out of the integrating sphere IS through the outlet window WOr and the lens LN is measured. The light Li entering the integrating sphere is reflected by the region Wa uniformly in all directions, and the total amount of the reflected light is P.multidot.r, of which the amount of the light that hits the region Wr is P.multidot.r.multidot.a/S=P.multidot.r.multidot.k.sub.1, and the amount Ir.sub.1 of the light that is reflected by the region Wr to emerge out of the outlet window WOr is given as EQU Ir.sub.1 =P.multidot.r.multidot.k.sub.1 .multidot.r.multidot.k.sub.2. (1)
On the other hand, the amount of the light that is reflected by the region Wa in the directions other than toward the region Wr is P.multidot.r(1-k.sub.1). The light reflected by the region Wa in the other directions is reflected for the first time by the inner surface of the integrating sphere and the total amount of the reflected light is P.multidot.r(1-k.sub.1)r, of which the amount of the light that hits the region Wr is P.multidot.r(1-k.sub.1)r.multidot.k.sub.1, and the amount Ir.sub.2 of the light that is reflected by the region Wr to emerge out of the outlet window WOr is given as EQU Ir.sub.2 =P.multidot.r(1-k.sub.1)r.multidot.k.sub.1 .multidot.r.multidot.k.sub.2. (2)
The light reflected for the first time by the inner surface of the integrating sphere IS is again reflected by the inner surface of the integrating sphere. The amount Ir.sub.3 of the light reflected for the second time to hit the region Wr to be reflected thereby to merge out of the window WOr is given as EQU Ir.sub.3 =P.multidot.r(1-k.sub.1)r(1-k.sub.1)r.multidot.k.sub.1 .multidot.r.multidot.k.sub.2. (3)
In a similar manner reflection of the light is repeated, so that the total amount Ir of the light taken out of the window WOr is the sum of the amounts Ir.sub.1, Ir.sub.2, Ir.sub.3, . . . and given as ##EQU1##
Then, the light measuring device comprising the lens LN, the aperture AP and the photodetector PD is transferred to the other outlet window WOs so that the sample SM is aligned with the window WOs and the light measuring device.
At this time in a manner similar to the above-mentioned manner in which the amount Ir is obtained, the amount Is of the light that emerges out of the sample light outlet window WOs is given as ##EQU2##
It should be noted here that the light entering the integrating sphere IS and being reflected for the first time by the region Wa is intercepted by the screen SC so that it does not impinge on the sample SM. Therefore, the light that impinges on the sample for the first time is the light reflected by the region Wa and then reflected by the inner surface of the integrating sphere, and the amount of this light is given as P.multidot.r.sup.2 .multidot.k.sub.1. Of this light the amount Is.sub.1 that is directed to the outlet window WOs is given as EQU Is.sub.1 =P.multidot.r.sup.2 .multidot.k.sub.1 .multidot.r'.multidot.k.sub.2. (6)
This amount corresponds to the amount Ir.sub.1 of the reference light given as the equation (1). Dividing the amount Is by the amount Ir, we obtain the absolute reflectance r'.
Therefore, if the amount Ir is measured with the light measuring device positioned in front of the outlet window WOr and the amount Is is measured with the measuring device positioned in front of the outlet window WOs, the ratio between the two measured values will give the absolute reflectance r' of the sample.
As can be easily understood, in order to measure the two values it is necessary to move the measuring device between the two outlet windows WOr and WOs. This not only requires a troublesome operation but also makes the whole structure of the apparatus large in size so that it is very difficult to design the apparatus as an optional accessory for use in a spectrophotometer. If an individual light measuring device is provided in front of each of the two outlet windows, it would not be necessary to move the light measuring devices. However, there is no other means to compensate for inherent difference in sensitivity between the two measuring devices than to exchange the relative positions of the two devices, and exchanging their positions would make the provision of two measuring devices meaningless.